In this paper, we investigate the semi-online scheduling problem with known maximum job size on two uniform machines with the speed ratio s >= 1. The objective is to minimize the makespan. Two algorithms are presented, where the first is optimal for 1.559 <= s <= 2 and s >= 3+root 17/2 . In addition, the improvement on lower bounds is made for 2 < s < 3+root 17/2.